Solihull south of Birmingham I think is the nicest area. The town centre is nice, it's safe...a bit expensive, but it's well spent I think. And it's really easy to get to B'Ham city centre, especially if just don't want to drive and just hop on the train into Moor Street or Snow Hill.
As for north Birmingham, I live in Great Barr right now. Don't like it much and I'm planning on moving to Solihull soon. However, Sutton Coldfield is nice, Four Oaks is extremely nice and expensive, Streetly as well. Check out
http://www.upmystreet.com. It's a great site to get neighbourhood info by using its postal code.